The questions are as follows:
1. Which of the following is an equation?
a) x^2 + y^2 > 10.
b) x^2 - 2y^2
c) x^2 + y^2 = 10.
d) Both a and c
2. Which of the following is not an expression?
a) (x + 1)(x - 1)
b) (x + 1)/(x - 1)
c) 1 + 1 + 1 + 1 + 1 + 1 + 1
d) x + 1 = x - 1
3. Which of the following is an expression?
a) a = b
b) The answer is 22.
c) a^2 + 2ab + b^2
d) x > 300
4) Which of the following is not an equation?
a) 14 = 10
b) x = 10
c) x^2 = 10
d) x^2 - 10
5) Which of the following expressions is equivalent to the expression (x + 1)(x - 1)?
a) x^2 - 2x - 1
b) x = 1
c) x = 1 or x = -1
d) x^2 - 1
6) Which of the following equations is equivalent to the equation 4x + 2 = 6?
a) 4x = 4
b) 1
c) 4x + 2
d) 4x = 8
The answers to the questions are as follows:
1) The answer is c). Option a) is an inequality, and option b) is an expression, not an equation. An equation must be a complete mathematical statement with an equals sign.
2) The answer is d). Option d) is an equation, not an expression. The remaining options are expressions.
3) The answer is c). Option c) is an expression, representing a quantity without making a complete statement. The remaining options are all complete mathematical statements, hence they are not expressions.
4) The answer is d). Option d) is an expression, not an equation. The remaining options are equations. Even though the statement in option a) is false, it is still an equation.
5) The answer is d). Options b) and c) are incorrect since we are looking for an expression, not an equation, which is equal to the expression given. That is what it means for expressions to be equivalent. Multiplying x + 1 and x - 1 gives the expression x^2 - 1.
6) The answer is a). An equivalent equation is an equation that has the same truth value as a given equation. Put in other words, One equation can be deduced from the other. The equation in option a) can be deduced from the original equation by subtracting 2 from both sides.
Further explanations are as follows:
An equation in math always has an equals sign. In the language of mathematics, an equation is a complete sentence stating that two values or quantities are equal. An expression is more like a phrase, as it describes some value or quantity without making any assertion about it.
Two expressions are equivalent if they are equal. Two equations are equal if one can be deduced from the other.
